In conventional projection apparatus, an image, provided from an essentially flat image-forming surface, is projected onto an essentially flat display surface. In film-based projection, for example, light is transmitted through a flat piece of film for projection onto a flat movie screen. Digital image-forming devices, such as transmissive and reflective LCDs and digital micromirror devices (DMDs) similarly produce an image on a flat surface. This allows projection apparatus employing these devices to use output optics that are similar to the projection optics employed in film-based projectors.
A number of optical systems, however, form images using curved surfaces, particularly optical systems of the immersive type that are designed to provide a wide field of view. One example system of this type is disclosed in commonly assigned U.S. Pat. No. 6,416,181 (Kessler et al.) and U.S. Pat. No. 6,522,474 (Cobb et al.), both incorporated herein by reference, herein referred to as either the '181 or '474 patent. In an autostereoscopic imaging apparatus 10 as described in the '181 disclosure and as shown in FIG. 1, a curved mirror 24 is employed, in combination with a beamsplitter 16 for providing an autostereoscopic virtual image to a viewer 12 at left and right viewing pupils 141 and 14r. For each viewing pupil 141 and 14r, an image generation system 70 provides an initial intermediate curved image that is then projected through a ball lens assembly 30 in order to form a left or right intermediate curved image at a focal plane of curved mirror 24.
The monocentric optical apparatus of the '181 disclosure provides autostereoscopic imaging with large viewing pupils, a very wide field of view, and minimal aberration. In order to provide this type of imaging and take advantage of the inherent benefits of monocentric projection, the apparatus of the '181 disclosure, given its source image formed on a flat surface, must form an intermediate image having a suitable curvature. Referring to FIG. 2, there is shown, extracted from the more detailed description of the '181 disclosure, a portion of an image generation system 70 for providing an intermediate curved image 80 for projection, for either eye, in autostereoscopic imaging apparatus 10. Here, an image generator 74 provides a source image from an image source 94, where image source 94 has a flat surface, such as from a reflective LCD. A relay lens 54 directs light from image generator 74 onto a diffusing element 32, so that a curved intermediate image 76 is formed on a diffusive surface 40. Ball lens assembly 30, cooperating with beamsplitter 16, projects curved intermediate image 76 toward a front focal surface 22 of a curved mirror 24 to form intermediate curved image 80. Curved mirror 24 then provides a virtual image of intermediate curved image 80 at viewing pupil 14.
Using the overall arrangement of FIG. 2, image source 94 can be any of a number of image sources that emit light, such as a transmissive or reflective LCD spatial light modulators, a digital micromirror device (DMD) spatial light modulator, a CRT, or an OLED or PLED device, for example. Significantly, the image formed on image source 94 is substantially flat. There may be some slight curvature to this image, such as would be provided by a CRT; however, the arrangement of FIG. 2 works well when image source 94 is flat and shows how intermediate image 80 can be formed having the needed curvature. Since most image display devices form a flat image, there is, then, no need for modification to off-the-shelf display components with this arrangement.
As the '181 disclosure points out, forming an intermediate image on a diffusive surface helps to overcome limitations imposed by the LaGrange invariant. A product of the size of the emissive device and the numerical aperture, the LaGrange invariant determines output brightness and is an important consideration for matching the output of one optical system with the input of another. Use of the diffuser with the '181 apparatus is necessary because the image-forming device, typically a reflective LCD or other spatial light modulator, is a relatively small emissive device, measuring typically no more than about 1 inch square. Referring again to FIGS. 1 and 2 and to the '181 disclosure, in order to maximize the light output from image generator 74, it is necessary to provide a large angle of emitted light, using diffusing element 32, in order to adequately fill left and right viewing pupil 141 and 14r. Diffusive surface 40 is shaped to provide curved intermediate image 76 having the desired curvature for the projection optical system.
While use of a diffusing element 32 provides a workable solution for forming a curved image, there are some drawbacks to projecting an image onto a diffusive component. In order to understand drawbacks with particular impact upon autostereoscopic imaging apparatus 10, it is instructive to consider how ball lens assembly 30 operates. Referring to FIG. 3a, there is shown the concentric arrangement and optical behavior of a ball lens assembly 30 for directing light from a curved image 50. A central spherical lens 46 is disposed between meniscus lenses 42 and 44. Central spherical lens 46 and meniscus lenses 42 and 44 have indices of refraction and dispersion characteristics intended to minimize on-axis spherical and chromatic aberration, as is well known in the optical design arts. An aperture stop 48 defines a ball lens pupil 106 within ball lens assembly 30. Aperture stop 48 need not be a physical stop, but may alternately be implemented using optical effects such as total internal reflection. In terms of the optics path, aperture stop 48 serves to define an entrance pupil and an exit pupil for ball lens assembly 30.
In most embodiments, meniscus lenses 42 and 44 are selected to reduce image aberration and to optimize image quality for the projected image projected. It must be noted that ball lens assembly 30 could comprise any number of arrangements of support lenses surrounding central spherical lens 46. Surfaces of these support lenses, however many are employed, would share a common center of curvature with Cball, the center of curvature of central spherical lens 46. Moreover, the refractive materials used for lens components of ball lens assembly 30 could be varied, within the scope of the present invention. For example, in addition to standard glass lenses, central spherical lens 46 could comprise a plastic, an oil or other liquid substance, or any other refractive material chosen for the requirements of the application. Meniscus lenses 42 and 44, and any other additional support lenses in ball lens assembly 30, could be made of glass, plastic, enclosed liquids, or other suitable refractive materials, all within the scope of the present invention. In its simplest embodiment, ball lens assembly 30 could simply comprise a single central spherical lens 46, without additional supporting refractive components.
In ideal operation, curved image 50 shares the same center of curvature Cba11 as ball lens assembly 30. When arranged in this fashion, light from any point on curved image 50 is imaged with minimal aberration, as is represented in FIG. 3a. 
The inherent advantages of a ball lens can be exploited using a modified design that employs a partial ball lens segment, such as using an hemisphere combined with a folding mirror, as is shown in the cross-sectional ray diagram of FIG. 3b and described in the '474 patent. In FIG. 3b, a hemispheric lens assembly 60 comprises a hemispheric central lens 66, one or more optional meniscus lenses 42, and a reflective surface 62 along the meridional plane of the hemisphere. Reflective surface 62 may be formed over the full surface of the meridional plane or may be formed only along a portion of this surface. As shown in FIG. 3b, hemispheric lens assembly 60 forms, from curved image 50 as its object, a curved image 64, folding the optical path at the same time. This arrangement can have advantages, for example, where space for optical components is constrained.
Referring to FIG. 4, there are shown ray traces of principal rays for projected light from image generation system 70. Light along optical axis 0 is incident to diffusing element 32 at a normal angle. As the projected light becomes off-axis, the incident angle onto diffusing element 32 also changes. At the edge of the projected field, as shown at an off-axis ray 200, the incident angle varies significantly from normal. This has a number of undesirable effects, as is shown in FIGS. 5a and 5b. Both on-axis light, as shown in FIG. 5a, and off-axis light, as shown in FIG. 5b, strike diffusing element 32 and are spread over a wide range of angles. The problems of most interest include the following related behavior:                (i) Hot spot. As a comparison of the clusters of rays in FIGS. 5a and 5b suggests, a higher percentage of on-axis light is provided to ball lens assembly 30 than of off-axis light; the result is a hot spot along optical axis O. Solutions for minimizing this effect include mechanical dithering of diffusing element 32; however, this type of solution adds cost for dithering components and requires further design compensation for high-frequency vibration effects.        (ii) Only a fraction of off-axis light reaches central spherical lens 46 for projection. Other light may be scattered throughout the optical system, reducing contrast.        
As FIGS. 5a and 5b show, providing diffused light over a wide angle is necessary in order to obtain at least some level of brightness from off-axis light. At the same time, however, wide angle diffusion reduces contrast due to stray light leakage. Thus, even given some amount of curvature, diffusing element 32 is constrained with respect to efficiency. The requirements for large angle diffusion add complexity and cost to the design of diffusing element 32. Thus, although the use of curved diffusing element 32 helps to surmount LaGrange invariant limitations, there is still room for improvement in contrast and brightness and a need to minimize or eliminate any hot spot effects. Of particular value would be methods that provide these performance improvements at low cost and with minimum complexity.
Thus, it can be seen that there is a need for an imaging subsystem that provides, from a substantially flat image source, a curved image having high brightness as an intermediate image for projection and display apparatus.